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Finance Calc Kit
Converters

Periodic Interest Rate Calculator

Calculate the periodic interest rate per compounding period from the annual nominal rate. Free online tool for daily, monthly, quarterly, and other compounding periods.

Nominal rate inputs

%
Common nominal rates:

Periodic interest rate

1.5000%

Rate per compounding period (P = R / m)

Nominal annual rate

18.00%

Stated annual rate (R)

Effective annual rate (EAR)

19.5618%

With m = 12 compounding periods

Step-by-step calculation

Convert a stated nominal annual rate into the periodic rate and effective annual yield.

  1. Given values

    Nominal annual rate R = 18.0000%, compounding frequency m = 12 per year.

  2. Periodic interest rate

    P=RmP = \frac{R}{m}

    P = 18.0000% / 12 = 1.500000% per period.

  3. Effective annual rate

    EAR=(1+P)m−1\text{EAR} = (1 + P)^m - 1

    EAR = (1 + 1.500000%)^12 - 1 = 19.5618%.

Report tool

Convert annual nominal rate to periodic interest rate

Banks and lenders quote a nominal annual interest rate, but interest often compounds monthly, quarterly, or daily. The periodic interest rate is the portion of that annual rate applied at each compounding interval. Knowing the periodic rate is essential for loan amortization, savings projections, and bond coupon calculations.

To convert an effective annual rate back into a stated nominal rate, use the nominal interest rate calculator. To compare yields across different compounding schedules, try the APY calculator.

Periodic rate formula

P=RmP = \frac{R}{m}
  • P: periodic interest rate per compounding interval
  • R: stated nominal annual rate
  • m: number of compounding periods per year

Effective annual rate (EAR)

Because interest compounds each period, the effective annual rate is higher than the nominal rate when m is greater than 1:

EAR=(1+P)m−1\text{EAR} = (1 + P)^m - 1

EAR reflects the true annual yield after compounding within the year. It is the figure regulators often require for deposit disclosures.

Worked example

A credit card quotes 18% nominal annual interest compounded monthly (m = 12):

  1. Periodic rate: P = 18% / 12 = 1.5% per month
  2. Effective annual rate: EAR = (1 + 0.015)^12 - 1 ≈ 19.56%

The 1.5% monthly rate is what gets applied to your balance each billing cycle. The 19.56% EAR shows the true annual cost after monthly compounding.

Frequently asked questions

What is the difference between nominal and effective rate?
The nominal rate is the stated annual rate before compounding effects. The effective annual rate (EAR) shows the actual annual yield or cost after interest compounds within the year.
How do I choose the compounding frequency?
Match the frequency stated in your loan, savings account, or investment contract. Monthly compounding (m = 12) is common for mortgages and credit cards. Quarterly (m = 4) is typical for bonds.
Is periodic rate the same as APR?
APR is usually quoted as an annual nominal rate. The periodic rate is APR divided by the number of compounding periods per year. Fees may also affect the true cost beyond the stated APR.
Why is EAR higher than the nominal rate?
Each compounding period earns interest on prior interest. More frequent compounding within the same nominal rate produces a higher effective annual yield.
Can I use this for daily compounding?
Yes. Select daily (365) compounding and the calculator divides the annual nominal rate by 365 to get the daily periodic rate.
Are my inputs stored?
No. Calculations run entirely in your browser. URL parameters let you share a specific rate and compounding scenario.

Resources and references

The formulas and methods in this calculator were checked against these independent sources.